Cats (Felis silvestris catus) and dogs (Canis lupus familiaris) are the most common companion animals in the world. In Ukraine, as a result of the war, the number of stray animals has sharply increased, and the development of a shelter system has become especially relevant. Shelter veterinary medicine requires objective criteria for assessing animal adaptation, as new conditions—particularly changes in diet—can cause stress and deteriorate health. This study proposes to evaluate the so-called rehabilitation potential (RP)—the likelihood of full rehabilitation of an animal’s body within a given period, based on a quantitative analysis of deviations of hematological and biochemical blood parameters from the norm. RP was assessed on the following scale: “High” (0–24% deviations), “Medium” (25–49%), “Low” (50–74%), and “Very low” (75–100%). The health status of cats and dogs was examined on the first day, the 30th day, and the 60th day of their stay in the shelter. In cats, according to hematological parameters, RP increased from “Very low” (92.3%) on day 1 to “High” (15.4%) on day 60; according to biochemical parameters—from “Low” (61.1%) to “High” (22.2%). Body weight increased from 1.12±0.11 kg to 2.21±0.12 kg (P≤0.05). In dogs, hematology-based RP changed from “Very low” (76.9%) to “Medium” (30.8%), and biochemistry-based RP—from “Very low” (77.8%) to “High” (5.55%). A comparison of different feeds (Premium, Holistic, Super Premium) showed that in cats, the best results were achieved with Premium and Holistic feeds (“High” RP), while Super Premium resulted in a “Medium” RP. In dogs, Holistic feed was the most effective (“High”), Premium produced “Medium” (hematology) and “High” (biochemistry) results, while Super Premium showed “Low” and “Medium” results. Comparative analysis revealed species-specific differences in adaptation: significant differences were found in 45.5% of hematological, 58.3% of biochemical, and 75.0% of leukocyte indices. By day 60, most animals’ parameters were within the normal range, indicating that this period is sufficient for full rehabilitation. The most informative adaptation criteria for both species were leukocyte count, segmented and band neutrophils, monocytes, leukocyte shift index, neutrophil-to-lymphocyte ratio, and Harkavy’s adaptation index; for dogs additionally—the nuclear shift index. Among biochemical parameters, the most valuable for cats were total protein, cholesterol, globulins, inorganic phosphorus, LDH, and alkaline phosphatase; for dogs—total protein, albumins, globulins, cholesterol, urea, creatinine, AST, GGT, LDH, and CPK. The proposed method allows for a quantitative assessment of animal adaptation, monitoring shelter performance, and improving the welfare of stray cats and dogs.